By \(\mathbb {Z}_{n}\)  we denote the abelian group of order \(n\) .
For \(p_{1}=2\) , the signed graph \(\Sigma \) , is a disconnected sigraph with two connected
components, say \(\Sigma _{1}\)  and \(\Sigma _{2}\) , where
\(V(\Sigma _{1})=\lbrace (1, v)| v~is~odd\rbrace \cup \lbrace (0, v)| v~is~even\rbrace \)  and
\(V(\Sigma _{2})=\lbrace (0, v)| v~is~odd\rbrace \cup \lbrace (1, v)| v~is~even\rbrace \) .
Since every Cayley graph \({\mathrm {Cay}}(G, S)\)  is \(|S|\) -regular (see for example [1]}),
we find that \(\Sigma \)  is \(|\Phi |\) -regular.
